In my view, we are allowing the government to frame the immigration problem for us. We must consider that in some cases, such as here, the government is not acting in our own individual best interest.
Thus, the term "illegal" associated with "alien" or "immigrant" is one of the government's invention.
What we as individuals must do is look at the problem from our own perspective. It is my understanding that this has not been done very often and has not be heralded very effectively.
The reality is that foreign nationals are in every recognized nation worldwide, creating a nearly fully integrated polyglot. To somehow require all these people to get their "papers in order" with respect to the local laws of each country is crazy.
There has to be a better, more accommodating, and global solution. Like a national identity card that is accepted worldwide. This different than a passport and should be a smart card with various data on it relevant to the bearer and the country he or she hails from.
Take a look at the end-to-end treatment of the immigration problem that has been prepared by Trigon-International, Inc. This is actionable, affordable, and feasible and more aptly it addresses the problem in situ meaning that the fix goes in without having to reset the pieces on the game board.